MNRAS 446, 3608–3620 (2015)
doi:10.1093/mnras/stu2319
The frequency and nature of ‘cloud–cloud collisions’ in galaxies
C. L. Dobbs,1‹ J. E. Pringle2 and A. Duarte-Cabral1
1 School
of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
of Astronomy, Madingley Road, Cambridge CB3 0HA, UK
2 Institute
Accepted 2014 October 30. Received 2014 October 30; in original form 2014 September 3
ABSTRACT
Key words: stars: formation – ISM: clouds – ISM: evolution – galaxies: ISM.
1 I N T RO D U C T I O N
Cloud–cloud collisions have long been thought to play an important
role in both the growth of molecular clouds, and potentially the star
formation rate in galaxies. However, the nature of cloud–cloud collisions, how we identify them, and whether they are sufficiently frequent to contribute to cloud growth, are still unanswered questions.
Establishing examples of cloud–cloud collisions observationally is
difficult, and even those studies which claim to find cloud–cloud
collisions are not definitive.
Many early papers proposed cloud–cloud collisions as a means
of building up more massive giant molecular clouds (GMCs) from
smaller molecular clouds (Field & Saslaw 1965; Scoville, Solomon
& Sanders 1979; Norman & Silk 1980; Kwan & Valdes 1983,
1987; Tomisaka 1984, 1986; Roberts & Stewart 1987). One criticism of this earlier work was that the expected time-scale between
cloud–cloud collisions was very long, of the order of 100 Myr or
more (Blitz & Shu 1980). It was subsequently proposed (Casoli
& Combes 1982; Kwan & Valdes 1983; Dobbs 2008) that cloud–
cloud collisions would be enhanced in spiral arms. Calculations in
E-mail: [email protected]
the 1980’s modelling clouds orbiting a galaxy found an enhancement of a factor of a few in the spiral arms (Kwan & Valdes 1983;
Tomisaka 1984) though they include neither hydrodynamics or selfgravity. Dobbs (2008) carried out hydrodynamic calculations, but
did not quantitatively investigate the effect of spiral arms on cloud–
cloud collisions. Tasker & Tan (2009) computed the frequency in
hydrodynamic calculations of galaxies with no spiral potential, obtaining a frequency of 1 collision per 1/4 orbit. They do not discuss
in depth why this differs by up to an order of magnitude from
the theoretical work, but do argue that self-gravity is important in
their calculations. With an imposed spiral and bar potential, Fujimoto et al. (2014) find merger rates as high as 1 every 2 or 3 Myr
(1 collision per 1/40th of an orbit).
Cloud–cloud collisions have also been supposed to be important
for star formation. The Schmidt–Kennicutt relation can be expressed
in a form which includes the angular velocity, (Wyse 1986; Wyse
& Silk 1989; Silk 1997; Kennicutt 1998; Tan 2000). In this instance,
if the star formation rate is assumed to arise from cloud–cloud collisions, then these will be proportional to the shear of the disc, leading
to a Schmidt relation of the form SFR ∝ where is the star
formation efficiency. Recently, Inoue & Fukui (2013) have also suggested that cloud–cloud collisions lead in particular to massive star
formation (see also discussion in Longmore et al. 2014). A number
C 2014 The Authors
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We investigate cloud–cloud collisions and giant molecular cloud evolution in hydrodynamic
simulations of isolated galaxies. The simulations include heating and cooling of the interstellar medium (ISM), self-gravity and stellar feedback. Over time-scales <5 Myr most clouds
undergo no change, and mergers and splits are found to be typically two-body processes, but
evolution over longer time-scales is more complex and involves a greater fraction of intercloud material. We find that mergers or collisions occur every 8–10 Myr (1/15th of an orbit)
in a simulation with spiral arms, and once every 28 Myr (1/5th of an orbit) with no imposed
spiral arms. Both figures are higher than expected from analytic estimates, as clouds are not
uniformly distributed in the galaxy. Thus, clouds can be expected to undergo between zero and
a few collisions over their lifetime. We present specific examples of cloud–cloud interactions
in our results, including synthetic CO maps. We would expect cloud–cloud interactions to be
observable, but find they appear to have little or no impact on the ISM. Due to a combination
of the clouds’ typical geometries, and moderate velocity dispersions, cloud–cloud interactions
often better resemble a smaller cloud nudging a larger cloud. Our findings are consistent with
the view that spiral arms make little difference to overall star formation rates in galaxies, and
we see no evidence that collisions likely produce massive clusters. However, to confirm the
outcome of such massive cloud collisions we ideally need higher resolution simulations.
Giant molecular cloud interactions
transfer of mass between different time frames, and thus typically
refer to collisions as mergers, as they involve mass transfer from
two clouds into one. In Section 2.2, we define five categories of
cloud evolution. In Section 3, we show how clouds are divided into
these categories, and over what time-scales. In Sections 3.2 and 3.5,
we determine cloud–cloud collision rates with and without strong
spiral structure, respectively, and compare both these measures to
theory in Section 5. In Section 4, we investigate collisions/merger of
massive clouds, and show specific examples from our calculations.
In Section 6, we examine how one of our cloud mergers appears in
H2 and CO.
2 D E TA I L S O F S I M U L AT I O N S A N D M E T H O D
The simulations used in this paper are presented in Dobbs & Pringle
(2013) and Dobbs, Pringle & Naylor (2014). These previous papers,
and Dobbs, Burkert & Pringle (2011) show that the simulations
reproduce well the large-scale properties of the ISM (e.g. amounts
of gas in cold and warm phases, scaleheights), and properties of
GMCs, compared to observations. The simulations are computed
using the smoothed particle hydrodynamics code SPHNG (Benz et al.
1990; Bate, Bonnell & Price 1995; Price & Monaghan 2007). We
show results for two simulations, with and without a spiral potential.
Otherwise the simulations have the same parameters. The surface
density in each case is 8 M pc−2 , and the number of particles
8 million, giving a mass per particle of 312.5 M . The calculations
include self-gravity, cooling and heating (from Glover & Mac Low
2007), and stellar feedback (from Dobbs et al. 2011) with a star
formation efficiency of 0.05. Star particles are not included in the
simulations, there is only gas. The calculations include H2 (Dobbs
2008) and CO (Pettitt et al. 2014) formation. Both calculations
include a logarithmic potential to provide a flat rotation curve;
one calculation also includes the spiral potential of Cox & Gómez
(2002). Most of the results we show are for the case with the spiral
potential. The spiral is imposed from t = 0 in the simulations, and
our analysis is carried out at a time of 250 Myr. The two calculations,
with and without a spiral potential, are shown in Fig. 1.
Whilst we predominantly show results for the simulations above,
we briefly mention a simulation with a higher surface density of
16 M pc−2 , to appear in Duarte-Cabral et al. (2014), in Section 4.
This otherwise has the same feedback, cooling and heating as the
other simulations. This calculation used only 4 million particles.
Further resolution studies, and tests of the feedback implementation in these models are shown in Dobbs (2014), where we model
a section of a disc at much higher resolution. In Dobbs (2014), we
Figure 1. Column density plots for two simulations used in this paper
are shown above, at a time of 250 Myr. The calculation shown in the lefthand panel includes an N = 2 imposed spiral perturbation, whereas for the
calculation shown in the right-hand panel, gas is only subject to a symmetric
logarithmic potential.
MNRAS 446, 3608–3620 (2015)
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of observations of massive star clusters also display evidence that
they have formed as the result of cloud–cloud collisions (Stolte et al.
2008; Furukawa et al. 2009; Torii et al. 2011; Fukui et al. 2014).
In addition to the massive clusters above, a number of nearby
smaller molecular clouds are thought to be in the process of colliding (Galván-Madrid et al. 2010; Higuchi et al. 2010; Duarte-Cabral
et al. 2011; Nakamura et al. 2012). The colliding clouds are primarily identified by blue and redshifted velocity fields. There is still
some uncertainty as to whether these truly are cloud–cloud collisions, as the velocity fields are often quite complex, and may also
reflect internal motions within the clouds. Nevertheless, we would
statistically expect to see at least some cloud–cloud collisions in
the galaxy, so some of these examples may well be truly colliding.
Colombo et al. (2014) also consider the properties of GMCs in arm
and interarm regions in M51, and suggest that differences in the
mass function may reflect the occurrence of cloud–cloud collisions
in the spiral arms.
As well as global numerical, or analytic studies of cloud–cloud
collisions, there have been calculations of individual cloud–cloud
collisions. These calculations have different predictions for the outcome of collisions. In some cases, cloud–cloud collisions can be
quite violent, and largely destroy the natal clouds. This tends to be
the case if the clouds collide with large Mach numbers, or velocities of at least several km s−1 (Hausman 1981; Lattanzio et al. 1985;
McLeod, Palouš & Whitworth 2011). Although some previous work
has considered the nature of collisions of different impact parameter (Taff & Savedoff 1973; Lattanzio et al. 1985), the frequency
of different impact parameters has not been considered in a global
context. It is also not clear from the simulations so far what is the
impact of collisions on the star formation rate, i.e. whether star formation increases (or even decreases) compared to isolated clouds;
however, the above studies indicate that it may depend highly on
the nature of the collision.
Whilst we have so far discussed cloud–cloud collisions, this picture does not reflect that the interstellar medium (ISM) is a continuous medium. We can only hypothesize cloud–cloud collisions (and
indeed clouds themselves) by introducing some density cut off to
define cloud boundaries. In reality, surrounding regions of the ISM
will be interacting at lower densities than the cloud boundary. In
such a scenario, the ‘collision’ represents a converging flow, with
likely increasing densities and decreasing sound speeds, until the
cloud boundary is reached. The literature perhaps has also reflected
the uncertainty of cloud–cloud interactions. There are various terms
to denote the interactions of clouds – collisions, coalescence, mergers, agglomeration. Collisions are often used for all types of interaction, whereas coalescing clouds and mergers assume that the two
clouds definitively join together. The term collision can often imply quite a violent interaction, though we note that this is probably
not the case for molecular clouds. We further note that collisions
can have any impact parameter. The term ‘agglomeration’ was used
in Dobbs (2008), and one or two other works, which is perhaps
more indicative of random shaped objects sticking together than a
collision.
In this paper, we consider the nature of cloud evolution, in particular focusing on cloud mergers and their frequency. Compared
to previous work, we provide a much more rigorous framework
to identify cloud–cloud collisions, which is necessary when clouds
evolve in time and space. In Dobbs & Pringle (2013), we highlighted
the complexity of following the evolution of clouds in simulations,
the frequent interactions, clouds splitting apart, or merging together
as they evolve. These issues were in addition to the basic problem
of how to define a cloud. Here, we define interactions in terms of the
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C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
are able to resolve clouds with 80 times more particles than shown
here. These high-resolution simulations verify the cloud properties
(and properties of the ISM) found in the global models, and do not
show a strong dependence on the details of stellar feedback. However because of the smaller coverage area, they contain too small a
number of GMCs for the type of analysis we present here.
2.1 Cloud selection
Figure 2. The particles are plotted for a small section of the galaxy (left)
and again at a time of 0.1 Myr later (right). The middle panel shows a cloud
as selected by the ‘grid-based’ clump-finding algorithm. There are evident
changes in the structure of the cloud even over a 0.1 Myr time frame, and
the net change in mass is 10 per cent. The bottom panels show clouds found
using the ‘density-based’ clump-finding algorithm (using ρ min = 50 cm−3
and l = 10 pc). The cloud is indistinguishable between the two time frames,
as would be expected over such a short time period, and the net change in
mass is 0.1 per cent. The ‘density-based’ algorithm is 3D, so some particles
which may look like they should be part of the cloud in 2D may be further
above or below the cloud particles in 3D.
MNRAS 446, 3608–3620 (2015)
ρ min (cm−3 )
50
10
l (pc)
10
15
(M pc−2 )
45 ± 10
13 ± 3
Per cent of gas in clouds
3.3
17
ρ(H2 )min (cm−3 )
l (pc)
(M pc−2 )
Per cent of gas in clouds
10
15
45 ± 10
2.8
no significant changes over 0.1 Myr. However, the clump-finding
algorithm picks out noticeably different structures (middle panels).
When this algorithm is used, a cloud appears to change on shorter
time-scales than supposed by the actual particle distribution. We
checked whether or not selecting clouds in the rotating frame of the
potential contributed to this problem, but this was not found to have
a big impact, rather the error lies in the conversion to a grid.
Instead, here we adopt a ‘friends of friends’ algorithm, which
is non-grid based. We first select particles over a given (volume)
density, ρ min . We then group together all particles within a given
length-scale (l). This naturally produces clouds in 3D. There is some
degeneracy between the density criterion ρ min , and l, i.e. increasing ρ min gives very similar results to decreasing l. We again show
the evolution of a cloud over 0.1 Myr in Fig. 2 (lower panels). Unlike with the grid-based approach, there is negligible change in the
structure of the cloud over such a small time-scale, as would be
expected. We use this method for the rest of the paper.
In Table 1, we show different parameters used to find clouds in
the simulation. We select two separate populations of clouds, with
different densities and surface densities. For our fiducial results,
we take ρ min = 50 cm−3 and l = 10 pc (where ρ reflects the
total density). This gives clouds with a range of surface densities a
little low compared to typical surveys, but similar to the Galactic
12
CO clouds observed by Heyer et al. (2009). The fraction of the
total gas which lies in clouds is very small with these criteria,
hence we also investigated clouds found using ρ min = 10 cm−3
and l = 15 pc. As this yields clouds of unrealistically low surface
densities compared to molecular clouds, the second criterion is
mostly simply a comparison. However, this could correspond to
collisions of H I clouds, for example in the colliding flow scenario
(e.g. Vázquez-Semadeni et al. 2007). Having a higher fraction of
gas in clouds would also better reflect regions such as the inner
parts of the Galaxy. For both cases, we only consider clouds with
masses over 1.5 × 104 M , or over 50 particles. We repeated
our analysis with higher mass limits, which also serves as a check
for any dependence on resolution, but found similar results (see
Section 4). Though obviously for calculating merger frequencies for
massive clouds compared to the total number of clouds (see again
Section 4), taking different lower limits for the massive clouds will
yield different answers.
2.2 How can clouds evolve?
For simplicity we assume that interactions, evolution or fragmentation of clouds are typically at most a two-body process. We can
check the validity of this assumption later. But with this in mind,
we can divide the possible evolution of clouds into a number of
categories; ‘No change’, ‘Merge’, ‘Create’, ‘Destroy’ and ‘Split’.
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In previous work (Dobbs et al. 2014; Dobbs 2008), we used a gridbased approach to identify clouds, whereby we selected grid cells
above a given surface density and group together all adjacent cells
as a ‘cloud’. However, whilst this grid-based approach is sufficient
for identifying clouds at a single snapshot (see Dobbs, submitted),
we found it proved less suitable for studying clouds over time. This
is because of the error associated with identifying cloud boundaries with a grid-based approach. We show an illustration of this
problem in Fig. 2, where we plot two clouds, identified 0.1 Myr
apart. By looking at the particle distribution (top panels), we find
Table 1. Table of the parameters associated with cloud selection. ρ min
and l are parameters used to identify clouds (see text). Then, shows the
average surface density of the clouds identified, and the standard deviation. The fraction of the total gas which lies in clouds is also shown. The
lower part of the table shows parameters used when taking the molecular
density rather than the total density, see Section 5.
Giant molecular cloud interactions
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such that they are decreasing, i.e. f1 ≥ f2 ≥ f3 . . . . We also define
∞
fi , the amount of gas which was not in any cloud
f0 = 1 − i=1
at time T0 . We can then consider how a population of clouds will
evolve, in this case from the time T0 . For this, we define gj as the
fraction of a cloud existing at time T0 which ends up in a cloud j at
time T1 (see Fig. 3). We again rearrange g in order of decreasing gj ,
and similarly define g0 = 1 − j∞=1 gj , the fraction of gas converted
back into the intercloud ISM.
Using these definitions of f and g, we can then define the following categories of cloud evolution:
Merge:
f1 , f2 > 0
Create: fi = 0 ∀ i > 0 and
Destroy: gj = 0 ∀ j > 0
Split:
and
f0 > 0
g0 > 0
g1 , g2 > 0.
No change + Split: fi = 0 ∀ i > 1 and
No change + Merge: gj = 0 ∀ j > 1
Figure 3. This cartoon illustrates our definitions of f and g. Clouds are
represented by rectangles, which are subdivided into fi and gj , and the ellipses
represent intercloud ISM. The top panel represents backward evolution. This
particular example shows a merger. The fi indicate how gas in the cloud at
T1 was distributed in clouds and intercloud medium at time T0 . The lower
panel shows forward evolution, and represents a split. Here, the gj indicate
how the gas in a cloud at T0 is distributed in clouds and intercloud medium
at T1 .
These represent all the possible outcomes between two different
time frames. We determine the evolution of the clouds, and the
numbers of clouds in each of these categories, by studying populations of clouds at two time frames, T0 and T1 , where T1 = T0 + T.
In all the cases, here we take T0 = 250 Myr. We can either study evolution forwards in time, or backwards in time, each giving different
information about cloud formation, interactions or destruction. For
example, mergers are obtained from the backward evolution of the
clouds, whereas splits are obtained from the forward evolution.
To determine how a population of clouds has evolved, we consider the origin of clouds selected at time T1 . For each cloud at
time T1 , we define fi as the fraction of that cloud which was in
some cloud i defined at time T0 (see Fig. 3). We rearrange the fi
f1 > 0
and g1 > 0
which cover unions of the categories mentioned earlier. Note that
categories Create, Merge and No change+Split cover all possible
origins of clouds at T1 , whilst Destroy, Split and No change+Merge
cover all possible evolution of clouds from T0 . With these auxiliary
categories, and our initial assumption that splits or merges only
involve two clouds, we can then determine the number of clouds in
the ‘No change’ category as
No change NNC : = NNC+S − 2NS
or
NNC+M − 2NM .
Again, we have a check on the two-body assumption.
In practice, we identify clouds in these various categories by
searching through the clouds at T0 and T1 to find those which contain
the same particles. For example, if multiple clouds at T0 contain
the same particles as a cloud at T1 we identify this as a merger.
Similarly, multiple clouds at T1 that contain particles common to
only one cloud at T0 are identified as a split. Clouds which have
been destroyed exist at T0 but have no counterpart at T1 , whilst
created clouds exist at T1 but have no counterpart at T0 .
As mentioned above, for the present we ignore fi and gj with
i, j > 2. This is partly motivated by finding that in practice most
mergers or splits only involve two clouds (see Section 3.1), and the
fi and gj with i, j > 2 tend to be negligible anyway. We find with
this assumption that the number of merges and splits is reduced
by 5–10 per cent for T = 1 Myr (compared to the total number
without the two-body assumption), makes negligible difference for
smaller time-scales, and leads to about a 20 per cent reduction for
MNRAS 446, 3608–3620 (2015)
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The ‘Create’ category describes clouds that do not exist at time
T0 which appear by time T1 , whilst conversely ‘Destroy’ describes
clouds which exist at T0 , but whose material has returned to the
intercloud medium by T1 . If we are assuming that cloud evolution
involves no more than two bodies, then we consider a ‘Merge’
to occur when two clouds present at T0 have merged into a single cloud at T1 . Similarly a split occurs when one cloud present
at T0 has split into two clouds at T1 . We define the number of
clouds created as NC , the number destroyed as ND , and the number of mergers and splits as NM and NS , respectively. Note that
N(T1 ) − N(T0 ) = NC + NS − ND − NM and that this gives a check
on the two-body assumption.
We have not yet assigned a ‘No change’ category. This is complicated because this category requires knowing about the forward
and backward evolution simultaneously, whereas we only know the
gj at time T0 and fi at time T1 . At this point it is helpful to introduce
two auxiliary categories:
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C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
T = 5 Myr. In addition, we have not made any constraints about
the quantities f1 , f2 , g1 , g2 in the above categories. For example a
cloud which has a small but non-zero f1 or g1 is probably not well
represented by the ‘No change’ category as it must have undergone
a considerable increase or decrease in mass. However, this is typically not the case, and the interactions and evolution can largely
be considered exclusively from the intercloud medium, except for
over long time periods. We could require that ‘No change’ requires
f1 , g1 over a certain value, though this would be somewhat arbitrary. Instead we note that, similar to neglecting interactions of >2
clouds, there is likely some uncertainty on the fractions of different
categories we obtain, again likely a few per cent for T = 1 Myr,
negligible for lower times, and higher for longer times.
3 H OW D O C L O U D S E VO LV E ?
3.1 Cloud mergers and splits in more detail
Figure 4. The nature of the evolution of clouds is shown over time periods
of 0.1, 0.4, 1, 2 and 5 Myr (top panel), according to the categories defined in
Section 2.2. Bars indicate the number of occurrences of each category. Over
short time-scales, clouds typically undergo no change, as expected. Merges
and splits occur in roughly equal numbers and are less frequent than cloud
creation or destruction simply from the non-cloud ISM. The lower panel
shows the number of clouds in each category when taking ρ min = 10 and
50 cm−3 , and T = 1 Myr.
MNRAS 446, 3608–3620 (2015)
In this section, we consider the values of fi and gj for clouds, and
thus the validity of our assumption so far that cloud interactions are
typically two-body processes.
In Fig. 5, we show f1 , f2 and f3 , the fractions of clouds at 250 Myr
which now lie in clouds at 251 Myr. The top panel shows results with
our fiducial density criteria, the lower panel with the low surface
density criteria. Because there are so many clouds, individual bars
are not easily distinguishable, but the cases where bars for f1 and
f2 are present indicate that a merger has taken place. The blank
space above each bar indicates f0 . The figure is clearly dominated
by the f1 ’s. This is as expected, as we would expect most clouds to
undergo little change over a 1 Myr time interval, and exhibit high
f1 . As described in the previous sections, the cases with f1 > 0 but
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We first show the number of different cloud outcomes according
to the categories defined in the previous section. We show these in
Fig. 4 for different time intervals (top panel) and, different density
criteria with a time period of 1 Myr (lower panel). As expected, over
a time period of 0.1 Myr, the clouds almost universally undergo no
evident evolution. As the time period increases, mergers and splits,
cloud creation and cloud destruction become more frequent. Note
that each merger involves two clouds merging, and likewise each
split involves one cloud splitting in two. Generally, the number
of clouds which are created from the intercloud medium (Create
category) and destroyed back to intercloud medium are higher than
the number of new clouds spawned from splits, or which disappear
through mergers. Fig. 4 also demonstrates that typically the number
of merges and splits are similar. This could be time dependent,
e.g. when cloud growth is predominant at the early stages of the
simulation, mergers are likely to be more frequent than splits. At
the current stage, there is more of a tendency for massive clouds to
be broken up, and there is a net increase in the number of clouds,
although the system is overall in equilibrium over longer timescales (see Dobbs & Pringle 2013 section 5.1.2 for a discussion of
massive clouds forming and dispersing in the arms). The sum of all
categories is not consistent because we are including both clouds
which are created and destroyed, thus we obtain a sum which is
greater than either the number of clouds at T0 or T1 especially over
longer time periods.
As mentioned earlier, for now we only include mergers or splits
involving two clouds, leading to an underestimate of the number
of mergers. Conversely including any instance of f2 or g2 > 0,
however small, is likely an overestimate. Our assumption of at most
two-body interactions is less accurate over longer time-scales. Over
5 Myr, interactions involving more clouds become more frequent,
suggesting that a cloud may have undergone multiple interactions
with other clouds (or splits). We tend to focus much of our analysis
on time-scales of 1 Myr, which appears a reasonable time-scale to
identify interactions between pairs of clouds, though there is not
necessarily a single suitable time-scale for all clouds. The duration
over which two clouds collide will vary as l/σ v where l is some
typical length scale of the cloud and σ v is the cloud–cloud velocity
dispersion. We also find interactions of smaller clouds are more
frequent. Therefore, interactions between smaller clouds (in the
sense of both the time-scales between interactions and the duration
of interactions) may occur over shorter time-scales. The time-scale
of 1 Myr is sufficient to capture most interactions of both large and
small clouds.
We also show in Fig. 4 (lower panel) results when using different
density criteria for selecting clouds. For the lower density criteria,
there are more clouds which undergo no change, splits and mergers.
By contrast, the number of clouds created and destroyed is comparatively smaller. This is not so surprising as with the lower density
criterion, much more of the gas lies in clouds, so there is less exchange between cloud and intercloud material, and more clouds are
formed as the result of splits, or undergo mergers, than form solely
from intercloud material.
Giant molecular cloud interactions
f2 , f3 = 0 etc. will mostly fall in the ‘No change’ category, and a
few in the ‘Split’ category.
There are clear examples in Fig. 5 of clouds which lie in the
‘Merge’ category, exhibiting two or three bars indicating non-zero
f2 , and in a few cases non-zero f3 . The number of instances of a
non-zero f3 are clearly small. There are only about 10 visible cases
in the figure, as indicated by the magenta bars. In most cases, the
f3 are also quite small. This justifies assuming that interactions are
at most a two-body process, as we did for the previous section, at
least over a 1 Myr time-scale. Again, over longer time-scales this
assumption becomes invalid. We also notice that the mergers are
typically on the left-hand side of the plot, with lower values of f1 .
This is again as expected, because we would tend to expect clouds
to evolve without significant change in f1 , unless they interact with
another cloud (or unless those clouds are low density or low mass
and near the cloud detection criteria). In the simplest case, of a
merger of two equal mass clouds, we would expect f1 and f2 to
be ∼0.5. There are mergers similar to this indicated in Fig. 5 (with
perhaps f1 , f2 ∼ 0.4). There are also cases where f1 f2 .
In the lower panel of Fig. 5, we show f1 , f2 and f3 for our lower
density criteria, again over a 1 Myr time period from 250 to 251 Myr.
Figure 6. This figure indicates where gas in clouds ends up over a 1 Myr
time period. Clouds at a time of 250 Myr are shown along the x-axis. The
y-axis indicates the fractions of gas in these clouds at 250 Myr which ends up
in clouds at 251 Myr (g1 , g2 , g3 in order of decreasing size) and intercloud
medium (the blank space above each column). The panels show the cases
where ρ min = 50 (top) and 10 (lower) cm−3 .
The main difference is that there is less blank space, i.e. f0 is smaller.
This again reflects that more of the gas is in clouds, so there is less
gas from the intercloud medium which is involved with cloud evolution. This is similar to the finding that with the lower density criteria,
mergers and splits are relatively more frequent, whilst created and
destroyed clouds are less frequent. For the lower surface density
criteria, the f3 are barely visible, indicating again that interactions
typically involve only two clouds. Although not evident from the
figure, the main exceptions are one or two very massive (107 M )
clouds which undergo more mergers with a larger number of small
clouds. Lastly, in Fig. 6, we show the distribution of g1 , g2 and g3 ,
this time indicative of where gas ends up after a 1 Myr time period. We again show plots for our standard density criteria (top) and
lower density criteria (lower panel). The plots are dominated by g1
indicating that most clouds evolve unperturbed. Clouds which split
tend to have lower g1 , similar to the f1 for mergers. Again, instances
with non-zero g3 are rare indicating that clouds typically split up
into only two components.
3.2 Frequency of cloud–cloud mergers
As mentioned in the Introduction, the frequency of cloud–cloud
collisions is an important diagnostic to determine their relevance to
GMC formation in galaxies. Using our analysis, we can estimate the
MNRAS 446, 3608–3620 (2015)
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Figure 5. This figure indicates how much gas arises in each cloud at
251 Myr from clouds and intercloud medium over a 1 Myr time period.
Clouds at a time of 251 Myr are shown along the x-axis. The y-axis indicates
the fractions of gas in the resultant clouds at T = 251 Myr from clouds
present at 250 Myr (f1 , f2 , f3 in order of decreasing size) and intercloud
medium (the blank space above each column). The panels show the cases
where ρ min = 50 (top) and 10 (lower) cm−3 .
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C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
frequency of cloud mergers. We determine the frequency of cloud
mergers as
f =
No. clouds involved in mergers
2NM
=
Myr−1
Total number of clouds
N (T0 )
(1)
3.3 How much gas arises from cloud versus intercloud
medium?
Figs 5 and 6 indicate that generally clouds evolve with little interaction with intercloud medium, at least over 1 Myr. However, we
would expect this to change over longer time-scales. We show in
Fig. 7 the median value of the sum of the fi , or equivalently 1 − f0 ,
over different time-scales. We also show separately results for all
clouds, and those just for mergers. As expected, minimal gas in
clouds originates from the intercloud medium for small T. Over
all clouds, for T = 1 Myr, the median value of f0 is 7 per cent,
or equivalently 93 per cent of gas arises from cloud and 7 per cent
from intercloud material. However by 5 Myr, half of cloud material
originates from intercloud material. Thus, gas is being exchanged in
Figure 7. This figure indicates how much gas of clouds existing at T1 was
present in clouds at T0 , for a given T, described by i fi (effectively how
much gas stays in clouds over a time period T). Results are shown for all
clouds (red points) and just those which are the product of mergers (blue
points). For time-scales of 1 or 2 Myr, gas stays in clouds. However for
time-scales of 5 Myr, there is much more mixing of cloud and intercloud
gas, and above 5 Myr the majority of gas in a cloud originates in intercloud
material. The bars indicate the lower and upper quartiles.
MNRAS 446, 3608–3620 (2015)
3.4 Typical values of f1 and f2
Fig. 5 showed mergers of two or more clouds, but it is difficult to
tell whether mergers are typically between clouds of equal mass, or
smaller clouds joining larger clouds. In Fig. 8, we show the numbers
of mergers for different ratios of f2 /f1 , again with T = 1 Myr.
Overall Fig. 8 indicates that the majority of mergers have small
f2 compared to f1 . If f2 /f1 1, this implies either that a small
cloud has merged with a much larger cloud, or that two more equal
mass clouds have collided, but only a small fraction of one has
merged with the other. The latter could arise from a grazing, or
offset collision of two clouds. To differentiate between these two
scenarios, we have divided the mergers in Fig. 8 into two populations
depending on the original mass of the clouds colliding. We divide
mergers depending on whether the ratio of the original masses,
denoted m2 /m1 , is greater or less than 0.5. If m2 /m1 > 0.5, then
the clouds merging had similar masses. Fig. 8 indicates that for
those mergers with f2 /f1 1, typically m2 /m1 < 0.5 indicating that
a small cloud is merging with a large cloud. There are relatively
few cases of two similar mass clouds interacting, but only a small
transfer of mass from one to the other. Similarly, most the mergers
with f2 /f1 ∼ 1 involve two similar mass clouds, rather than an
unequal mass transfer during the merger.
Again, we may expect the values of f1 and f2 , and the nature of
mergers, to be time dependent. For example a grazing collision of
two clouds, with only a small transfer of mass from one cloud to
Figure 8. The number of mergers is shown for different ratios of f2 /f1 , so
for example f2 /f1 ∼ 1 indicates roughly equal amounts of mass originate
from merging clouds. The clouds are further classified by the ratio of the
cloud masses of the merging clouds, m2 /m1 .
Downloaded from http://mnras.oxfordjournals.org/ at University Library on March 7, 2016
over a time period of 1 Myr. This definition of frequency represents
the frequency of mergers experienced by one cloud as it travels
around the galaxy (note that in reality the lifetime of the cloud may
be less than the time between mergers, see Section 3.6). We note that
it is possible that the clouds can collide and form multiple resultant
clouds, e.g. Clouds A and B can merge to produce Clouds C and
D. Here, we take care not to count the merger of Clouds A and B
twice, although the number of instances of this occurring was fairly
small. For our fiducial density criterion, if only including two-body
interactions, we find that 156 clouds are involved in interactions
over a 1 Myr period (out of a total of 1442), which gives 0.11 Myr−1 ,
roughly 1 every 10 Myr, or 1/14th of an orbit at R = 5 kpc. Including
mergers involving more than two clouds, the frequency is slightly
higher, 1 every 8 Myr or 1 every 1/17th of an orbit. We also evaluated
the merger frequency for our low surface density criteria, but did
not obtain noticeably different values.
clouds over a time-scale of several Myrs, in agreement with Dobbs
& Pringle 2013 where we found GMC lifetimes of the order of several Myrs. The sum of fi tend to be smaller for mergers compared
to cloud evolution generally, reflecting that f1 is typically lower for
mergers (Fig. 5) and mergers tend to involve more disruption. For
the longer time-scale, the opposite is true, i.e. mergers reflect a lower
fraction of intercloud material, perhaps indicating that mergers are
sustaining clouds over longer time periods. As expected the timescales for gas in clouds and intercloud gas to exchange is longer
with the lower density criterion (not plotted), in this case the amount
of gas retained in clouds after 5 Myr (1 − f0 ) is still over 70 per cent.
Again, this reflects similar findings by Dobbs & Pringle (2013) that
giant molecular associations are likely to have longer lifetimes.
Giant molecular cloud interactions
another, would be indistinguishable from a full merger of a smaller
cloud with a more massive cloud, when viewed over a short time
period. To test this, we looked at results for T = 5 Myr (not shown
in Fig. 8). In this case, a higher fraction (around ∼40 per cent)
of clouds with small f2 /f1 have more equal masses (m2 /m1 ∼ 1),
indicative of grazing collisions, though the majority still represent
the full merger of a smaller cloud.
3.5 Frequency of mergers without spiral arms
Figure 9. The values of f1 , f2 and f3 are shown over a 1 Myr time period,
for a simulation with no imposed spiral arms. These represent the fraction of
gas in clouds at a time of 251 Myr, which was present in clouds at 250 Myr.
Clouds at a time of 251 Myr are shown along the x-axis. The y-axis indicates
the fractions of gas f1 , f2 and f3 , in order of decreasing size, and intercloud
medium (the blank space above each column). The standard density criteria,
with ρ min = 50 cm−3 is used. The main difference compared to Fig. 5 is
that there are fewer blue bars present (for f2 ) indicating fewer mergers in the
absence of spiral arms.
3.6 Comparison of cloud merger rates with cloud lifetimes
In Dobbs & Pringle (2013), we analysed cloud lifetimes and concluded that most clouds have quite short lifetimes 10 Myr. Thus
for clouds in the spiral arms, we would expect most to only experience one or two mergers during their lifetime. However, in Dobbs &
Pringle (2013) we also noted that some clouds, including a number
of more massive 106 M clouds, exhibited lifetimes of 20 Myr or
more, and thus could undergo multiple mergers over their lifetime.
Fundamentally, we expect the lifetimes to be a result of clouds
merging, since this builds up mass into more massive and longer
lived clouds. In the spiral arms, clouds are stochastically able to
undergo multiple collisions, before stochastically being destroyed.
Conversely in the simulations with no spiral arms, the cloud merger
rate is small, at least for >104 M clouds. Thus, the probability of
acquiring a high mass, long-lived cloud is low.
4 MERGERS OF MASSIVE CLOUDS
As mentioned in the Introduction, collisions of more massive clouds
may be of particular interest as they may be associated with massive
star clusters. In particular, collisions may enable a large mass of gas
to be delivered to a massive, dense GMC in a short period of time,
thus accounting for small age spreads in massive clusters (Furukawa
et al. 2009; Fukui et al. 2014). In this section, we present and discuss
the examples of mergers of massive clouds, which are occurring at
our chosen time frame of 250–251 Myr, in the simulation with an
imposed spiral potential.
We first considered whether taking a higher mass cut off changed
our results in the earlier parts of the paper (how the clouds evolve,
and the fractions f0 , f1 , f2 ), but we did not find significant differences. We then calculated the frequency of mergers of more massive
clouds. Over a 1 Myr time period, taking ρ min = 50 cm−3 (this is
the total, atomic plus molecular density) to select clouds, we find
seven mergers of two or more clouds with masses >105 M , a frequency of 0.0049 Myr−1 , or one merger every 206 Myr (one every
one and one half orbital periods). The details of the mergers are
shown in Table 2, where we can see that one case involves three
clouds merging to form one cloud, the other cases only involve
two clouds. The last column indicates whether the interaction is
filamentary in nature (see Fig. 10). Because clouds are sometimes
elongated, and furthermore roughly aligned with the spiral arms,
mergers of this type are surprisingly frequent (compared to a distribution of randomly orientated clouds). Mergers not labelled as
‘filamentary’ involve more full on collisions between typically less
elongated clouds. The majority of our examples are ‘filamentary’
rather than ‘full on’ in nature.
Fig. 11 shows Merger 1, which involves one cloud of 5 × 105 M
and two clouds of ∼105 M . The most massive cloud is elongated,
aligned with the spiral arm. The two smaller clouds merge on to
the most massive cloud at one end. From the velocities, it seems
the far right cloud is moving downwards on to the centre cloud,
and the centre cloud is merging with the more massive, left-hand,
cloud. However, the far right cloud is actually moving away from
the far left cloud, so the three clouds do not appear to be totally
convergent. The merger of the three clouds results in an even further
elongated cloud (lower panel), with perhaps just a small increase
in dense gas in the centre. Thus, the collision does not appear to
have a strong impact on the structure of the clouds. The interaction
in Fig. 11 highlights the difficulty in proposing the collision of
massive clouds to produce large amounts of dense gas quickly.
Many of the clouds are elongated and aligned with spiral arms, so
MNRAS 446, 3608–3620 (2015)
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We also investigate cloud evolution in galaxies without a strong
spiral arm perturbation, and in particular the frequency of cloud
mergers. In this section, we analyse results from a simulation with
no imposed spiral potential. We find that over a 1 Myr period, 42
out of 1184 clouds are involved in interactions with each other. This
gives a frequency of 0.035 Myr−1 , once every 28 Myr, or once every 1/5 an orbit at a radius of 5 kpc. As expected, the frequency of
mergers is notably less compared to the simulation with spiral arms.
However, the interactions are still relatively frequent compared with
theoretical estimates (see Introduction and Section 5). This is because even without an imposed spiral potential, the gas gathers into
dense, sheared features like short sections of spiral arm, simply
due to self-gravity and thermal instabilities (see Fig. 1). Hence,
clouds are still concentrated into spiral-like features, rather than
being spread uniformly over the disc.
We also determined f0 , f1 , f2 and f3 as for Section 3.1, for the
case without spiral arms (see Fig. 9). Again, nearly all interactions
only involved two clouds. We found the median value of f0 was
9 per cent, indicating 91 per cent of gas stays in clouds compared
to 9 per cent from the intercloud medium. These fractions are quite
similar, just a slightly higher f0 , compared to the case with spiral
arms.
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C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
Table 2. Table showing the details of mergers between massive clouds. Mergers 1 and 2 are shown in Figs 11 and 12. The merger
velocities are calculated as the relative velocities between the two clouds (for Merger 1 two pairs of clouds are colliding). The mergers
occur predominantly in the plane of the disc, except for Merger 4.
Merger
Mass of first cloud
(105 ) M
Mass of second cloud
(105 M )
Mass of third cloud
(105 M )
Mass of resultant
cloud (105 M )
Filamentary?
Merger velocity
(km s−1 )
1
2
3
4
5
6
7
1.5
1.8
10.3
16.3
2.2
1.1
23
5.5
1.4
3.3
1.0
2.0
1.1
1.8
1.1
–
–
–
–
–
–
10.0
1.3
15.1
9.2
4.0
2.4
2.7
Y
N
Y
Y
N
Y
Y
17 and 8
3
8
2
4
9
8
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Figure 10. Possible orientations for mergers or collisions are shown. A
‘filamentary’ merger (a) is characterized by the intersection of the clouds
along the minor axis of the largest cloud. Examples of ‘full on’ mergers (b)
are characterized by intersection of the clouds along the major axis of the
largest cloud, or where neither of the clouds are particularly elongated (in
this paper elongated clouds have aspect ratio >2).
tend to interact along their minor axes (corresponding to Fig. 10,
top panel). Thus, they collide only over a small cross-section. The
density structure of the resultant cloud also suggests that rather
than a violent collision, the smaller clouds gently merge on to the
end of the larger cloud. The clouds could potentially reach high
densities where they collide but the collision interface not be fully
resolved by the simulations; however, the geometry of the collision
suggests that this would be limited to localized areas, and would
need higher resolution simulations to study in detail. The velocities
of the clouds are relatively high, compared to the other examples
(see Table 2, Figs 12 and 13). This could be conducive to triggering
star formation – simulations of isolated collisions have suggested
that higher Mach numbers produce a stronger shock compressed
layer, leading to higher rates of star formation (Bekki et al. 2004;
Kitsionas & Whitworth 2007). However, the relative velocities tend
to be higher for the filamentary collisions partly because the biggest
cloud simply covers a relatively large area spanning a wider range
of velocities.
MNRAS 446, 3608–3620 (2015)
Figure 11. ‘Merger 1’ (from Table 2) involving three clouds is shown at
250 Myr (top), before the clouds merge, and at 251 Myr (lower), when the
three clouds have merged into a more massive cloud. Details of the masses
of the clouds are given in Table 2. Arrows indicate the relative velocities of
clouds compared to the left-hand cloud. The boundaries of the clouds found
by the clump-finding algorithm are indicated by the thick purple lines. The
boundaries are drawn by hand – an automated method was tried first, but
the hand drawn boundaries gave more successful indications of the shapes
of the clouds compared to an automated method.
Giant molecular cloud interactions
in any figures) is the only other example which is not one cloud
joining the end of another. The clouds in this case appear more
intricately linked before the collision. Unusually, the clouds are in
an interarm spur. Whilst this does not necessarily rule out massive
cluster formation, it is counter-intuitive since these clouds are likely
at the end of their lifetime. Also these clouds tend to have a large
stellar age spread (Dobbs et al. 2014).
Our simulations highlight the difficulties of producing massive
clusters via collisions when considering that clouds are often elongated and collisions often represent the addition of a smaller cloud
at the end of one of these clouds. One possible limitation is that we
have used a relatively low surface density of 8 M pc−2 . Hence we
also analysed cloud mergers in a simulation with a surface density
of 16 M pc−2 (see Section 2), more similar to the inner Galaxy.
However, we tended to find not much difference from the mergers
shown in Table 2, with most still involving somewhat elongated
clouds, and little apparent change in cloud structure due to the collision. Another limitation is the maximum density imposed by the
inclusion of feedback, and that we cannot resolve the shock at the
interface of the collision, but much higher resolution simulations
would be needed to investigate this. Inoue & Fukui (2013) also
suggest that magnetic fields enhanced by shocks could promote
the formation of massive cores, but again this is far beyond the
resolution of galactic scale simulations.
5 T H E O R E T I C A L C O M PA R I S O N
As discussed in the Introduction, cloud–cloud collisions have been
the focus of a number of theoretical studies. We compare here
the frequency of mergers found in our simulations with results
expected from analytic estimates. To calculate collision, or merger
frequencies, we need the cloud–cloud velocity dispersion, so we
calculate that next.
5.1 Cloud–cloud velocity dispersions
Figure 13. Cloud–cloud velocity dispersions are shown for an average 1D
dispersion, the dispersion in the plane of the disc, and that in the vertical
direction. The dispersions tend to be at the lower end of observed values,
the median dispersion either averaged in 1D or in the plane of the disc being
around 4–5 km s−1 .
Fig. 12 shows a second example of a merger, both top down and
edge on. In the edge on view the clouds appear to merge more fully
compared to the top down view. Overall, similar to the collision in
Fig. 11, there is no particular indication that the cloud density structure is changed by the interaction. Rather the interactions resemble
two clouds coming together, but their own structures remaining
fairly similar. The relative velocity of the clouds is fairly small,
indicating only a mildly supersonic collision. Merger 5 (not shown
A number of works have considered the internal velocity dispersions
of clouds in galactic simulations (Tasker & Tan 2009; Dobbs et al.
2011), but here we determine cloud–cloud velocity dispersions. As
well as being a factor which governs the frequency, and possibly
nature of cloud–cloud collisions, we can also compare our cloud–
cloud velocity dispersions with observations.
Cloud–cloud velocity dispersions are shown in Fig. 13. The
velocity dispersions are calculated using the velocities of clouds
within regions of dimensions of 500 pc by 500 pc. Taking smaller
or larger regions shifted the dispersions to slightly (∼10 per cent)
lower and higher values, respectively, although once the size scale
reached 100 pc there were too few clouds to properly compute dispersions. We computed the dispersion in the plane of the disc (σ r ),
the mean 1D dispersion (σ 1D ), and the dispersion in the z direction
(σ z ). We find that in the plane of the disc the 1D dispersions are
around 3–6 km s−1 . By comparison, Wilson et al. (2011) find an average cloud–cloud velocity dispersion of 6.1 km s−1 from a sample
of nine galaxies, whilst a similar dispersion is found for the Milky
Way clouds (Stark & Lee 2005). Our 1D dispersions, which can be
compared to the 1D dispersions found by Wilson et al. (2011), are
generally smaller than the observations, but do compare favourably
with some galaxies with low dispersions such as NGC 628. We also
find that cloud–cloud dispersions are lower in the vertical direction,
compared to the plane of the disc. The relatively low values of the
velocity dispersions also suggest that most cloud–cloud interactions
will not be particularly disruptive. We also note that with a velocity
MNRAS 446, 3608–3620 (2015)
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Figure 12. ‘Merger 2’ (from Table 2) is shown at 250 Myr (top), before
the clouds merge, and at 251 Myr (lower), after the interaction. The lefthand plots show the xy (face on) view and the right-hand plots the yz (edge
on) view. Details of the masses of the clouds are given in Table 2. Arrows
indicate the relative velocities of the lower/left-hand cloud compared to that
on the top/right. This merger is also shown in H2 and CO in Figs 14 and 15.
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C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
dispersion of 6 km s−1 , a cloud will travel only about 6 pc Myr−1 ,
so short-lived clouds will only interact with other clouds formed in
a close proximity.
We also examined the cloud–cloud velocity dispersions in our
model without imposed spiral arms (not plotted). The distribution
of σ r , σ 1D , and σ z are similar but shifted roughly 1 km s−1 lower.
This could be because the spiral arms generally introduce slightly
larger velocity dispersions in the gas, due to spiral shocks (Bonnell
et al. 2006; Dobbs & Bonnell 2007; Dobbs et al. 2011). There is
also less difference between the velocity dispersion in the vertical
direction compared with the other velocity dispersions.
5.2 Cloud–cloud collision rates
tcoll =
1
λ
=
,
v
πr 2 nvc
(2)
where λ is the mean free path, r is the radius of the clouds, n is the
number density of clouds and v c the cloud–cloud velocity dispersion. The number density of clouds varies with Galactic radius, and
scaleheight above the disc. For simplicity, here we study the disc
within a radius of 5 kpc and take a scaleheight of 50 pc. This gives
a number density of 8.8 × 10−8 clouds per pc3 . Taking a typical
cloud radius of 50 pc and v c = 4 km −1 , we obtain tcoll ∼ 350 Myr.
This is similar to the estimate in Blitz & Shu (1980), though the
latter includes a gravitational term to increase the cross-section.
However, if we only select the clouds in the spiral arms, the number
density of clouds increases dramatically. By taking the arm width to
be 150 pc (a high estimate), and using the pitch angle, the volume
occupied by the arms is less than 5 per cent of the overall disc. As
the majority of clouds lie in the spiral arms, we obtain tcoll 20 Myr
(and λ 70 pc) if we only include the spiral arms, which is in much
better agreement with the results we find directly from the hydrodynamic calculations. Again, for the simulation without an imposed
spiral potential, we would expect a higher rate of collisions theoretically if we reduced the volume to reflect the clustered nature of
the clouds, compared to assuming a uniform distribution.
We do not consider the frequency of collisions of non-spherical
clouds here; however, collisions of non-spherical molecules have
been studied by Gopalakrishnan, Thajudeen & Hogan (2011). They
find an increase in the collision frequency by a factor of up to 5 for
highly elongated molecules.
6 S Y N T H E T I C O B S E RVAT I O N S O F M E R G E R S
In this section, we utilize the inclusion of H2 and CO in our models
to search for and show cloud mergers using a molecular rather
than total density threshold. We take a molecular density threshold
of 10 cm−3 (see Table 1) which is quite low, but the amount of
molecular gas at densities much higher than this is limited by our
inclusion of stellar feedback, and gas at total densities <100 cm−3
is not fully molecular. Thus, our molecular gas criteria is similar to
the criteria for total gas, because gas is often still not fully molecular
(note also that here we primarily consider CO velocity information
rather than intensities). We checked the frequency of mergers, and
the fractions f0 , f1 , f2 as for the earlier parts of the paper, and found
similar results compared to our fiducial analysis with a ρ min for
the total gas of 50 cm−3 . This is not so surprising, as the fraction
MNRAS 446, 3608–3620 (2015)
Figure 14. The merger of two massive clouds is shown, at times of 250 Myr
(top) and 251 Myr (lower) and in the xy plane (left) and the yz plane. The
colour density scale shows the H2 column density, which is overplotted
on the total column density in black and white. White contours indicate
the cloud boundaries. In this case, the clouds were selected based on H2
densities.
of gas in clouds, and surface densities of the clouds using these
different criteria are very similar. We also compared the example
massive cloud mergers as found in Table 2. We tend not to find
exactly the same mergers (though two were clearly identifiable
as the same mergers as in Table 2) indicating that the details of
interactions themselves may be sensitive to whether the total or
molecular density is used. However, we found a similar number
of interactions of massive clouds (and interactions in total) using
the molecular density criteria, and again most of the interactions
involved one very filamentary cloud, and another joining on the
end.
We show in Fig. 14 the merger shown in Fig. 12, but with clouds
found from the H2 density, rather than the total density. The merger
looks fairly similar to the case with the total density, but there are
subtle differences where the total density is high, but not the H2 ,
and vice versa.
To see how this merger appears in the CO (1–0) transition, we
post-processed the results from the simulation using the TORUS radiative transfer code (Harries 2000; Acreman et al. 2012, Duarte-Cabral
et al. 2014). In Fig. 15, we show the CO emission of these clouds in
xz space (not shown in Fig. 14) so that the line-of-sight component
of the velocity corresponds to the velocity along the y-axis, which
is the direction in which the two clouds are colliding (see Fig. 14).
In the xz plane, the clouds are not obviously physically separated,
but one is clearly at lower values of x compared to the other.
The plots showing the velocity field (left) clearly show two different velocities for the two clouds, which are kept even after the collision occurs, with a relatively strong velocity discontinuity where
the collision occurs (∼10 km s−1 ). These velocity field maps were
created by calculating the first moment of the CO emission, and
therefore, they do not recover all the complexity of the velocity
structure. One way to assess the complexity of the velocity structure, is by assessing the line-of-sight velocity dispersion (vy ),
calculated as the second moment of the CO emission (right-hand
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The time between collisions can be estimated theoretically from
the cloud–cloud mean free path. If we assume that the clouds are
spherical (and ignore gravity), then the time between collisions is
expected to be
Giant molecular cloud interactions
3619
ics of the clouds, which could potentially have an impact on the
star formation taking place (that we do not resolve with the current
resolution). We again note, as for Section 4, that the number of
highly resolved clouds where we can construct this kind of analysis
is limited by the resolution of the simulation.
7 CONCLUSIONS
plots of Fig. 14). These panels show a region of high, albeit localized velocity dispersion which is present after the collision but not
before, reaching as high as 20 km s−1 (more than doubling the original vy of the clouds). We also built a couple of position–velocity
cuts (not shown) running across this high velocity dispersion region
(at z ∼ 0.02 kpc), which confirm that the velocity structure before
the collision is quite simple, with smooth and clearly separated velocities, while the velocity structure after the collision shows two
or even three velocity components, where the velocity dispersion is
higher.
We note however that these signatures are only distinctive when
we can observe the collision along the collision axis. For instance,
our synthetic observations of the yz plane (also not shown) do
not show any significant change of velocity dispersions (along the
x-axis) after the collision, as there is minimal mixing along that axis.
As collisions in the Galaxy are rarely oriented along the observer’s
line of sight, the velocity discontinuity and velocity dispersion that
we estimate for this particular collision should be taken as indicative
(upper) limits of what would be observed, as they are measured
along the collision axis.
Overall, we find that such collisions do reproduce the signatures
that observers attribute to cloud–cloud collisions, such as velocity
shears with several overlapping velocity components (as seen in
position–velocity diagrams, e.g. Duarte-Cabral et al. 2010; Fukui
et al. 2014), and increased line widths (by more than a factor two).
Although most observations of cloud collisions in the Galaxy are
of lower mass molecular clouds and lower collision velocities (of
only a couple of km s−1 ) compared to the GMCs collisions we study
here, there is evidence of similar GMCs collisions in the Galaxy, as
that reported by Fukui et al. (2014), with a velocity discontinuity
of ∼15 km s−1 and v of 10 km s−1 .
In conclusion, although the morphology/density structure of
GMCs in the simulations do not suffer a great change due to a
collision event, collisions do have an impact on the global dynam-
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Figure 15. The merger of two massive clouds is shown, at times of 250 Myr
(top) and 251 Myr (lower) in CO(1–0) integrated intensities (black contours).
The colour scale shows v y (left) and the dispersion, v y (right). A velocity
gradient is clear where the clouds are colliding. There is also an increase
in the velocity dispersion after the clouds have collided. White contours
indicate the approximate boundaries of the clouds (from the particles).
We have studied the evolution of GMCs over short time periods
(0.1–5 Myr) using galactic simulations of the ISM. Cloud evolution
can be divided into a complete set of five categories: No change,
Create, Merge, Split, Destroy. Up to time-scales of 5 Myr, the most
frequent evolution of a cloud is ‘No change’. This time-scale also
corresponds to the time-scale over which the interaction of clouds
with intercloud material starts to become substantial, and needs to be
taken into account. A time-scale of 1 Myr is appropriate for studying
merges and splits, as these processes reduce to two-body problems
(longer timeframes allow multiple mergers and interactions). The
frequency of mergers of clouds >104 M is about one per 8–
10 Myr, or 1 per 15th of an orbit. This results in typically one merger
per cloud lifetime, possibly none for the shortest lived clouds or two
or three for longer lived (often more massive) clouds. In the absence
of spiral arms, this reduces to one merger per ∼28 Myr (1 per 1/5th
of an orbit, in good agreement with Tasker & Tan 2009). Both are
more frequent than previous analytic estimates, even in the case
without spiral arms, as clouds are unevenly distributed throughout
the galaxy.
Although we find that mergers or collisions are relatively frequent in the simulations, and at any point in time we can find a
number of examples as illustrated by Section 4, they do not appear
to have much impact. The reason for this is partly due to cloud
orientations, as clouds are often elongated, and aligned with spiral
arms. So, counter-intuitively, mergers are often prone to occur along
the minor axes of the clouds, rather than the major axes (where we
denote the minor axes in relation to the cross-section of the clouds,
as in Fig. 9a), thus only effecting smaller areas of the clouds. Furthermore, the velocity dispersions between clouds are not that high.
These factors mean that cloud mergers or collisions appear more
often simply as one cloud ‘nudging’ another, with little or no change
in the global density structure. Consequently, although the clouds
may ‘merge’ and the collective mass increases (and the global velocity field changes), there appears to be little mixing of the gas in
the two clouds. Rather each cloud retains its own characteristics.
An expression such as ‘collision’, which implies some significant
change to one or both clouds’ structures, may therefore be inappropriate to describe interactions of clouds, whilst ‘mergers’ or simply
‘interactions’ may be preferable. The cloud–cloud interactions also
do not resemble particularly the colliding flow scenario of cloud
evolution and star formation. Our picture is however in agreement
with previous studies (Elmegreen & Elmegreen 1986; Dobbs et al.
2011) which suppose that spiral arms make little difference to the
star formation rate, as the increase of cloud–cloud interactions we
find in spiral arms has little impact on the ISM, except to group
dense gas into larger structures.
Our simulations do not show any evidence that collisions of
massive clouds could be responsible for massive clusters. Although
the frequency of massive cloud interactions is not prohibitive (the
number of mergers roughly corresponds to the numbers of very
massive clusters), the interactions appear not be violent or quick
enough, and often involve involve small parts of the clouds. One
difference between the observations of massive cloud collisions,
and our simulations, is that the relative velocities of the observed
3620
C. L. Dobbs, J. E. Pringle and A. Duarte-Cabral
AC K N OW L E D G E M E N T S
The calculations for this paper were performed on the DiRAC
machine ‘Complexity’, and the supercomputer at Exeter, which
is jointly funded by STFC, the Large Facilities Capital Fund of BIS,
and the University of Exeter. Figs 2, 11, 12 and 14 were produced
using SPLASH (Price 2007). We thank the referee, Robi Banerjee, for
a helpful report which improved our explanations in some parts of
the paper. CLD acknowledges funding from the European Research
Council for the FP7 ERC starting grant project LOCALSTAR. CLD
thanks Thomas Henning, Annie Hughes, Steve Longmore and Jin
Koda for useful comments and discussions.
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collisions (e.g. 20 km s−1 ; Fukui et al. 2014) lie at the extreme end of
the examples we examine, and would expect from the cloud–cloud
velocity dispersions in our and nearby galaxies.
Lastly, we note some caveats to our results though that would
ideally be considered in future work. One caveat is that we do not
have the resolution to study cloud–cloud interactions in detail. In
particular, we are limited by the density threshold for adding feedback, so may miss large increases of density where the clouds collide. This could allow massive clusters of short age spreads, but our
simulations suggest this would only occur at the interface of considerably more extended clouds. We also have only a simple feedback
scheme. However most of our results, e.g. the relative frequency
of cloud mergers in different cases, the tendency of clouds to be
elongated and aligned when colliding, and the cloud–cloud velocity
dispersions, are not likely to depend strongly on feedback. Furthermore, Tasker & Tan (2009) achieve similar collision frequencies
with no stellar feedback. Our time-scale of 5 Myr, denoting when
cloud and intercloud material start to substantially may be more
subject to the details of feedback. A third caveat is that we have not
considered more extreme environments (e.g. galaxy mergers, highredshift galaxies, the Galactic Centre), which could potentially be
more conducive to more violent cloud–cloud interactions. We note
that of the observational and numerical studies related to massive
cloud–cloud collisions, a number concern Galactic Centre clouds
(e.g. Stolte et al. 2008; Hobbs & Nayakshin 2009; Johnston et al.
2014).